Journal of the Ramanujan Mathematical Society

Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

AF Equivalence Relations Associated to Locally Finite Groups


Affiliations
1 Department of Mathematical Science, Norwegian University of Science and Technology (NTNU), N–7491 Trondheim, Norway
     

   Subscribe/Renew Journal


In [5, Theorem 3.8], Giordano, Putnam and Skau showed that the ´etale equivalence relation associated to a (countable) group acting minimally and freely on the Cantor set is AF if and only if the group is locally finite. In this paper we answer what types of AF equivalence relations arise for such actions, linking them to Bratteli diagrams with the so-called equal path number property. Furthermore, we explore more general actions of locally finite groups, and we give a new and more transparent proof of a result by Krieger [9, Theorem 3.5 and Corollary 3.6] in the process.
User
Subscription Login to verify subscription
Notifications
Font Size

Abstract Views: 236

PDF Views: 0




  • AF Equivalence Relations Associated to Locally Finite Groups

Abstract Views: 236  |  PDF Views: 0

Authors

Heidi Dahl
Department of Mathematical Science, Norwegian University of Science and Technology (NTNU), N–7491 Trondheim, Norway

Abstract


In [5, Theorem 3.8], Giordano, Putnam and Skau showed that the ´etale equivalence relation associated to a (countable) group acting minimally and freely on the Cantor set is AF if and only if the group is locally finite. In this paper we answer what types of AF equivalence relations arise for such actions, linking them to Bratteli diagrams with the so-called equal path number property. Furthermore, we explore more general actions of locally finite groups, and we give a new and more transparent proof of a result by Krieger [9, Theorem 3.5 and Corollary 3.6] in the process.